Question

The height of a parallelogram is 10ft more than its base The area is 1200ft Solve b and h

Answer 1

Answer:

The answer is b = 30 ft and h = 40 ft.

Step-by-step explanation:

Given:

The height of a parallelogram is 10ft more than its base

The area is 1200 ft².

Now, to solve for b and h.

Let the base (b) be $x.$

And the height (h) is = $x+10.$

Area = 1200 ft².

Now, to solve we put formula of area:

$Area =b\times h$

$1200=x\times (x+10)$

$1200=x^2+10x$

Subtracting both sides by 1200 we get:

$0=x^2+10x-1200\\x^2+10x-1200=0$

Now, solving the quadratic equation:

$x^2+40x-30x-1200=0$

$x(x+40)-30(x+40)=0$

$(x+40)(x-30)=0$

$x+40=0$        and       $x-30=0$

Subtracting                  Adding both sides

both sides                    by 30 we get:

by 40 we get:      

$x=-40.$                           $x=30.$

So, we will take the positive result.

$x=30.$

Thus, the base (b) = 30 ft.

Now, getting the height (h) by substituting the value of $x$:

$x+10\\=30+10\\=40\ ft.$

Therefore, the answer is b = 30 ft and h = 40 ft.